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Unformatted text preview: MAE2381 Experimental Methods and Instruments Fall 2008 Project #1: Fourier series Assigned: 09/15/08 Due: 09/29/08 11:00 am This is a key assignment. If this key assignment is not submitted or passed, the student will not pass the class even if he/she scores perfectly on all exams and other assignments. No make-up will be given. Problem Statement : A periodic triangular wave signal as shown in the left graph can be defined as where T is the period. 1) Find the period T and the functions g 1 (t) and g 2 (t) based on the graph; 2) Derive the equation for the Fourier coefficients of this periodic wave signal; 3) Generate the periodic wave signal in Excel for [ ] T T t 2 , 2 − ∈ using a time increment δ t = T /20; 4) Calculate the Fourier coefficients A n and B n for n = 1, 2, … to 10 in Excel; 5) Generate the first five nonzero terms of the Fourier series using Excel for [ ] T T t 2 , 2 − ∈ using a time increment δ t = T /20; 6) Plot the periodic wave signal and the first partial sum of Fourier series in the same graph; 7) Plot the periodic wave signal and the 2nd partial sums of the Fourier series in the same graph; 8) Plot the periodic wave signal and the3rd partial sums of the Fourier series in the same graph; 9) Plot the periodic wave signal and the 4th partial sums of the Fourier series in the same graph; You can use example 2.4 and the attached solution for problem 2.16 (page 68) as reference. Submissions: 1) Expression of functions g 1 (t) and g 2 (t) (can be handwritten) (10 points) 2) Show the derivation steps for calculating the Fourier coefficients (can be handwritten) (20 points) 3) Printout of the first two pages of the Excel file showing a. time series t (10 points) b. the Fourier coefficients (10 points) c. the four graphs with proper format (10 points each) d. Excel format (10 points) ⎩ ⎨ ⎧ ≤ ≤ ≤ ≤ − = 2 / ) ( 2 / ) ( ) ( 2 1 T t t g t T t g t y-8-6-4-2 2 4 6 8-5 5 t(s) y(t)(v)-8-6-4-2 2 4 6 8-5 5 t(s) y(t)(v)-8-6-4-2 2 4 6 8-5 5 t(s) y(t)(v) Solution for PROBLEM 2.16 (on Page 68) KNOWN: y ( t ) = t for − 5 < t < 5 FIND: Fourier series for the function...
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- Spring '10
- Fourier Series, C D E F G H I J K L M N O, periodic wave signal